Quadratic Demand Research Articles

AN INVENTORY MODEL FOR NON-INSTANTANEOUS DETERIORATING ITEMS WITH QUADRATIC DEMAND RATE AND SHORTAGES UNDER TRADE CREDIT POLICY

In this paper, we propose an appropriate inventory model for noninstantaneous deteriorating items over quadratic demand rate with permissible delay in payments and time dependent deterioration rate. In this model, the completely backlogged shortages are allowed. In several existing results, the authors discussed that the deterioration rate is constant in each cycle. However, the deterioration rate of items are not constant in real world applications. Motivated by this fact, we consider that the items are deteriorated with respect to time. To minimize the total relevant inventory cost, we prove some useful theorems to illustrate the optimal solutions by finding an optimal cycle time with the necessary and enough conditions for the existence and uniqueness of the optimal solutions. Finally, we discuss the numerical instance and sensitivity of the proposed model.

Three-layered integrated inventory model for deteriorating items with quadratic demand and two-level trade credit financing

ABSTRACTIn this study, the three-layered integrated production – inventory model – is formulated in which a distributor and a retailer observe quadratic demand and a manufacturer runs the production proportional to the quadratic demand. The inventory of every player is subject to deterioration at a constant rate. The model considers two-level trade credit financing. The total cost of the integrated inventory system is minimised with respect to a number of shipments from the manufacturer to the distributor and the distributor to the retailer and each player's replenishment times. A solution procedure is worked out to obtain the best possible decision for the players of the supply chain. The results are validated with numerical examples for different scenarios. Managerial decisions are suggested.

An EOQ Model with Time Dependent Weibull Deterioration, Quadratic Demand and Partial Backlogging

This paper presents an order level inventory system with time dependent Weibull deterioration and quadratic demand rate where holding costs as a linear function of time. The proposed model considered here to allows for shortages, and the demand is partially backlogged. The model is solved analytically by minimizing the total inventory cost. The implementation of the proposed model is illustrated using some numerical examples. Sensitivity analysis is performed to show the effect of changes in the parameters on the optimum solution.

An inventory model for perishable items with quadratic trapezoidal type demand under partial backlogging

Article history: Received March 9 2014 Received in Revised Format August 5 2014 Accepted December 3 2014 Available online December 3 2014 In this paper, we consider the inventory model for perishable items with quadratic trapezoidal type demand rate, that is, the demand rate is a piecewise quadratic function under constant deterioration rate. The model consider allows for shortages and the demand is partially backlogged. The model is solved analytically by minimizing the total inventory cost. The result is illustrated with numerical example. Finally, we discuss sensitivity analysis for the model. © 2015 Growing Science Ltd. All rights reserved

An Inventory Model for Increasing Demand with Probabilistic Deterioration, Permissible Delay and Partial Backlogging

In this paper an inventory model for deteriorating items with time dependent quadratic demand and permissible delay in payments is developed. Shortages are allowed and are partially backlogged. An optimal policy that minimizes the total cost is developed. The objective of this study is to consider three different types of continuous probabilistic deterio-ration functions and to find the associated total cost. To illustrate the proposed model some numerical examples are given. Sensitivity analysis of the optimal solutions with respect to major parameters are carried out and comparison is made between the three models.

An Order Level Inventory Model for Deteriorating Items with Time – Quadratic Demand and Partial Backlogging

In this paper, a deterministic inventory model is developed for deteriorating items in which shortages are allowed and partially backlogged. The backlogging rate is assumed to be dependent on the length of the waiting time for the next replenishment. The longer the waiting time is, the smaller the backlogging rate would be. The deterioration rate is constant and demand rate is assumed to be time quadratic. Numerical example and sensitivity analysis are evaluated for validating the proposed model.

An Order Level Inventory Model for Deteriorating Items with Time – Quadratic Demand and Partial Backlogging

An Order Level Inventory Model for Deteriorating Items with Time – Quadratic Demand and Partial Backlogging

Optimal order quantity of retailer with quadratic ramp-type demand under supplier trade credit financing

This paper discusses the optimal ordering decision of the retailer influenced by the credit policy of the supplier under quadratic ramp-type demand. Based on the demand transfer point, four different models are proposed and their respective conditions for the existence and uniqueness of optimal solutions are verified. It is analytically established that the ordering decision of the retailer is greatly influenced by the trade credit period offered by the supplier under quadratic ramp-type demand. By comparing unit profit functions obtained under four different models, it is found that the preferable replenishment policy is always strictly determinable. The results are illustrated by numerical examples, and sensitivity analysis is also carried out.

Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays

The paper investigates the behavior of price differential equation model based on economic theory with two delays. The primary aim of this thesis is to provide a research method to explore the undeveloped areas of the price model with two delays. Firstly, we modify the traditional price model by considering demand function as a downward opening quadratic function, and supply and demand functions both depending on the price of the past and the present. Then the price model with two delays is established. Secondly, by considering the price model with one delay, we get the stable interval. Regarding another delay as a parameter, we studied the linear stability and local Hopf bifurcation. In addition, we pay attention to the direction and stability of the bifurcating periodic solutions which are derived by using the normal form theory and center manifold method. Afterwards, the study turns to simulate the results through numerical analysis, which shows that the provided method is valid.

An economic lot sizing production model for deteriorating items under two level trade credit

This paper develops an economic lot-sizing production model for deteriorating items with time dependent quadratic demand and delay in payments under two levels of trade credit policy. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer in turn provides customers a permissible delay period N. Cases where M < N and are investigated. In addition, the demand rate is assumed to be time and deterioration rate dependent quadratic demand. This paper deals with the problem of determining the optimal replenishment cycle length, optimal total cost and economic order quantity for an integrated inventory system under both two-level trade credit and time dependent quadratic demand rate. Numerical examples are presented to illustrate the developed model.

Deteriorated economic production quantity (EPQ) model for declined quadratic demand with timevalue of money and shortages

A deteriorating inventory model using time-value of money with price dependent declined quadratic demand is developed for a deterministic inventory system. This study applied the discounted cash flows (DCF) approach for problem analysis. The objective of this model is to maximize the net present value profit so as to determine the optimal time period and order quantity. The numerical analysis shows that an appropriate policy can benefit the retailer and that policy is important, especially for deteriorating items. Finally, sensitivity analysis of opti

An optimal inventory model for a deteriorating item with time - dependent quadratic demand and delay in payment for two warehouses

An optimal inventory model for a deteriorating item with time - dependent quadratic demand and delay in payment for two warehouses

A deteriorating inventory model for quadratic demand and constant holding cost with partial backlogging and inflation

In most of the deteriorating items inventory model, demand rate has considered as a constant function. But in realistic situation these cost varying according to time. So in this paper, we developed a deterministic deteriorating inventory model with inflation in which demand rate are quadratic function of time, deterioration rate is constant, backlogging rate is variable and depend on the length of the next replenishment, shortages are allowed and partially backlogged. The model is solved numerically by minimizing the total inventory cost for cycle. Keywords: inventory, deteriorating items, shortages, time dependent demand, partial backlogging, constant holding cost and inflation.

COMPLEX DYNAMICS AND CHAOS CONTROL IN NONLINEAR FOUR-OLIGOPOLIST GAME WITH DIFFERENT EXPECTATIONS

A dynamic four-oligopolist game characterized by firms with different expectations is modeled by four-dimensional nonlinear difference equations, where the market has a quadratic inverse demand function and the firm possesses a cubic total cost function. The Nash equilibrium of the local stability of the proposed model is studied. Then the bifurcation diagrams and Lyapunov exponents of the system are presented to show that four-oligopolist game model behaves chaotically with the variation of the parameters. Finally, the state variables' feedback and parameter variation method are effectively used to control the delay in the appearance of bifurcation.

Analysis of Constant Deteriorating Inventory Management with Quadratic Demand Rate

This paper investigates inventory-production systems where items fo llo w constant deterioration. The objective is to develop an optimal policy that min imizes total average cost. The quadratic demand technique is applied to control the problem in order to determine the optimal production policy, holding cost and cost of deterioration. Sensitivity analysis is conducted to study the effect of the cost parameters on the objective function.

An optimal replenishment policy for EOQ models with time-varying demand and shortages

While considering time dependent demand rate, most of the researchers developed their inventory models considering time dependent linear demand rate. Some models have been developed also by considering time dependent quadratic demand because by considering quadratic demand increasing, decreasing or constant all types of situations can be explained and hence it is more realistic than that of linear demand rate. But in the present paper, we have developed an EOQ model to describe an optimal replenishment policy with shortages and general time-varying demand instead of time dependent linear or time dependent quadratic demand. The successive replenishment cycle lengths are assumed to be reduced in arithmetic progression. The model is extended to the no shortage case also. The model is solved analytically to obtain the optimal solution of the problem. It is then illustrated with the help of numerical examples. The sensitivity analysis of the optimal solution towards changes in the values of different system parameters is also studied.

An EOQ model for a deteriorating item with time dependent quadratic demand and variable deterioration under permissible delay in payment

In a recent paper, Khanra, Ghosh and Chaudhuri’s (2011) presented an EOQ model for a deteriorating item with time dependent quadratic demand under permissible delay in payment. Deterioration considered in most of the EOQ models is constant, while in most of the practical cases the deterioration rate increases with time. This work is motivated by Khanra, Ghosh and Chaudhuri’s (2011) paper extending their model to allow for a variable rate of deterioration when delay in payment is permissible. The time varying demand rate is taken to be a quadratic function of time. For settling the account, the model is developed under two circumstances: case-1: The credit period is less than or equal to the cycle time and case-2: the credit period is greater than the cycle time. A numerical example is provided to illustrate the model. Sensitivity analysis has also been conducted to study the effect of the parameters.

Optimal pricing and ordering policy for an integrated inventory model with quadratic demand when trade credit linked to order quantity

PurposeThe purpose of this paper is to study integrated inventory system and pricing and ordering strategy for vendor‐buyer supply chain system. Here, the vendor offers a trade credit to the buyer when the buyer's order quantity exceeds a given pre‐specified quantity. Therefore, to incorporate the concept of vendor‐buyer integration and trade credit linked, the authors analyze the model to determine the optimal strategy for an integrated vendor‐buyer inventory system under the condition of credit linked to the order quantity when demand is quadratic.Design/methodology/approachA mathematical model for integrated inventory system is developed when demand rate is increasing function of the time and decreasing function of the retail price. By analyzing the total channel profit function, the authors developed some useful results to characterize the optimal solution and provide an iterative algorithm to find the retail price, buyer's order quantity and the number of shipments per production run from the vendor to the buyer.FindingsBy developing a solution algorithm, the optimal retail price, order quantity and number of shipments from the vendor to the buyer are provided. Numerical examples and sensitivity analyses are presented to validate the proposed model. Through extensive numerical analyses, it is observed that a longer credit term increases profits of the player for the entire supply chain. The vendor should establish the threshold for allowing trade credit comprehensively to ensure the greatest benefit for both players.Originality/valueMost of the research articles available in the literature considered the constant demand or linearly changing demand. In this paper, a mathematical model is developed considering time dependent quadratic demand. Very few researchers have investigated joint optimal policy in vendor‐buyer supply chain system, considering trade credit is linked to order quantity, and still there are not many findings on the benefit of integrated policy and trade credit.

An Inventory Model for Deteriorating Items with Quadratic Demand and Partial Backlogging

Aims: The scope of the model lies in its applicability in the management inventories of time-quadratic demand. It is also seen that large pile of goods displayed in a supermarket will motivate the customer to buy more. So the presence of inventory has a motivational effect on the people around it. Also there may be occasional shortages in inventory due to many reasons. Therefore, we develop an EOQ model for the inventory of a deteriorating item, taking demand rate and allowing shortages in inventory. Study Design: This paper presents an inventory model for deteriorating items with quadratic demand. In the model, shortages are allowed and partially backordered. The backlogging rate is a variable and dependent on the waiting time for the next replenishment. A numerical example is taken to illustrate the model and the sensitivity analysis is also studied. Methodology: Our purpose is to devise a mathematical model on inventory management taking all these factors into consideration. Results: Convexity condition of the cost function is established to ensure the existence of unique point of minimum. Conclusion: The proposed model can be extended in several ways. For instance, we may extend the demand function to stochastic fluctuating demand patterns or stock-dependent demand rate. Finally, we could extend the model to incorporate some more realistic features such as quantity discounts, permissible delay in payments, time value of money and inflation etc.

An EOQ Model for Deteriorating Items Quadratic Demand and Shortages

The scope of this model includes the application of inventory management. It has been empirically observed that the life expectancy of many items can be expressed in terms of Weibull distribution. This empirical observation has prompted researchers to represent the time to deterioration of a product by a Weibull distribution. It is also observed that demand of a consumer product usually varies with time and hence, the demand rate should be taken as time-dependent. Our purpose is to focus on a mathematical model on inventory production system considering all these factors. Therefore, we develop an economic inventory model for deteriorating items with quadratic demand and shortages in inventory.